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An empirical study of statistical properties of Choquet and Sugeno integrals

Author

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Éric Raufaste

    (CLLE-LTC - Cognition, Langues, Langage, Ergonomie - EPHE - École Pratique des Hautes Études - PSL - Université Paris Sciences et Lettres - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper investigates the statistical properties of the Choquet and Sugeno integrals, used as multiattribute models. The investigation is done on an empirical basis, and focuses on two topics: the distribution of the output of these integrals when the input is corrupted with noise, and the robustness of these models, when they are identified using some set of learning data through some learning procedure.

Suggested Citation

  • Michel Grabisch & Éric Raufaste, 2008. "An empirical study of statistical properties of Choquet and Sugeno integrals," Post-Print halshs-00445168, HAL.
    • Handle: RePEc:hal:journl:halshs-00445168
    DOI: 10.1109/TFUZZ.2008.917295
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00445168v1
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    References listed on IDEAS

    as
    1. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    2. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    3. Michel Grabisch, 2009. "Subjective Evaluation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00671303, HAL.
    4. Michel Grabisch & Ivan Kojadinovic & Patrick Meyer, 2006. "Using the Kappalab R package for Choquet integral based multi-attribute utility theory," Post-Print halshs-00186898, HAL.
    5. Marichal, Jean-Luc, 2006. "Cumulative distribution functions and moments of lattice polynomials," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1273-1279, July.
    6. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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    Cited by:

    1. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    2. Ünsal Özdilek, 2020. "Land and building separation based on Shapley values," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-13, December.

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